Multiple Case High Leverage Diagnosis in Regression Quantiles

Ranganai, Edmore; Vuuren, Johan O. Van; Wet, Tertius de

doi:10.1080/03610926.2012.715225

Cited by 7 publications

(3 citation statements)

References 26 publications

(37 reference statements)

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“…Additionally, it makes no distributional assumption regarding the error term, thus making it robust against heavy-tailed distributions and outliers. In other words, the quantile regression estimates the relationship between a set of covariates X and the conditional quantiles of Y, and it is useful in those applications in which boundaries also become important [48,49], as often it happens in environmental studies [50,51].…”

Section: Methods and Datamentioning

confidence: 99%

How Do Energy Use and Climate Change Affect Fast-Start Finance? A Cross-Country Empirical Investigation

et al. 2020

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To promote the sustainable development of developing countries through the reduction of greenhouse gas emissions and the impact of anthropogenic activity on the atmosphere, for some decades, developed countries and international institutions provided an increasing amount of climate financing tools, allocated through multiple channels. After the Copenhagen Conference of the Parties (COP15) held in 2009, developed country parties pledged to provide new and additional resources, including forestry and investments, approaching USD 30 billion for the period 2010–2012 and with balanced allocation between mitigation and adaptation. This collective commitment has come to be known as “Fast-start Finance” (FSF). To assess the key factors contributing to the amount and distribution of funding supporting projects using FSF, in this paper, we investigate the relationship between FSF, energy use, and greenhouse gas emissions. To this aim, two main analyses were carried out: (i) a qualitative examination of donor’s funding strategies and (ii) a quantitative analysis deepening the relationship between climate finance and greenhouse gas emissions by beneficiaries through a quantile regression model. Findings indicate a need to redesign the current aid scheme, and suggest an increasing need for financed projects to support sustainable economic innovation patterns of developing countries while paying close attention to the environmental policy context. The purpose was to provide useful feedback to policymakers to assess the effectiveness of the flow of funding for environmental plans and to avoid excessive aid dispersal and consequently a reduction of the FSF benefits.

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Section: Methods and Datamentioning

confidence: 99%

How Do Energy Use and Climate Change Affect Fast-Start Finance? A Cross-Country Empirical Investigation

et al. 2020

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“…In the design space, we consider four collinearity influential point scenarios in addition to the orthogonal design matrix and a correlated design matrix with high leverage points, while in the error term distribution scenarios, we consider the normal and heavy tailed (t−distribution cases at different degrees of freedom) distribution cases. The design matrices choices are simulated as in Jongh et al [14,28,29], viz.…”

Section: Simulation Design Scenariosmentioning

confidence: 99%

Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET

Mudhombo

Ranganai

2022

Computation

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Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression (QR) scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (X-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive LASSO and adaptive E-NET penalized QR (QR-ALASSO and QR-AE-NET) procedures where the weights are based on a QR estimator as remedies. We extend this methodology to their penalized weighted QR versions of WQR-LASSO, WQR-E-NET procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression (RR) parameter estimator. Although the use of this estimator may be plausible at the ℓ1 estimator (QR at τ=0.5) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a QR-based estimator to derive adaptive weights. We carried out a comparative study of QR-LASSO, QR-E-NET, and the ones we suggest here, viz., QR-ALASSO, QR-AE-NET, weighted QRALASSO penalized and weighted QR adaptive AE-NET penalized (WQR-ALASSO and WQR-AE-NET) procedures. The simulation study results show that QR-ALASSO, QR-AE-NET, WQR-ALASSO and WQR-AE-NET generally outperform their nonadaptive counterparts. At predictor matrices with collinearity inducing points under normality, the QR-ALASSO and QR-AE-NET, respectively, outperform the non-adaptive procedures in the unweighted scenarios, as follows: in all 16 cases (100%) with respect to correctly selected (shrunk) zero coefficients; in 88% with respect to correctly fitted models; and in 81% with respect to prediction. In the weighted penalized WQR scenarios, WQR-ALASSO and WQR-AE-NET outperform their non-adaptive versions as follows: in 75% of the time with respect to both correctly fitted models and correctly shrunk zero coefficients and in 63% with respect to prediction. At predictor matrices with collinearity masking points under normality, the QR-ALASSO and QR-AE-NET, respectively, outperform the non-adaptive procedures in the unweighted scenarios as follows: in prediction, in 100% and 88% of the time; with respect to correctly fitted models in 100% and 50% (while in 50% equally); and with respect to correctly shrunk zero coefficients in 100% of the time. In the weighted scenario, WQR-ALASSO and WQR-AE-NET outperform their respective non-adaptive versions as follows; with respect to prediction, both in 63% of the time; with respect to correctly fitted models, in 88% of the time while with respect to correctly shrunk zero coefficients in 100% of the time. At predictor matrices with collinearity inducing points under the t-distribution, the QR-ALASSO and QR-AE-NET procedures outperform their respective non-adaptive procedures in the unweighted scenarios as follows: in prediction, in 100% and 75% of the time; with respect to correctly fitted models 88% of the time each; and with respect to correctly shrunk zero 88% and in 100% of the time. Additionally, the procedures WQR-ALASSO and WQR-AE-NET and their unweighted versions result in the former outperforming the latter in all respective cases with respect to prediction whilst there is no clear "winner" with respect to the other two measures. Overall, the WQR-ALASSO generally outperforms all other models with respect to all measures. At the predictor matrix with collinearity-masking points under the t-distribution, all adaptive versions outperformed their respective non-adaptive versions with respect to all metrics. In the unweighted scenarios, the QR-ALASSO and QR-AE-NET dominate their non-adaptive versions as follows: in prediction, in 63% and 75% of the time; with respect to correctly fitted models, in 100% and 38% (while in 62% equally); in 100% of the time with respect to correctly shrunk zero coefficients. In the weighted scenarios, all adaptive versions outperformed their non-adaptive versions as follows: 62% of the time in both respective cases with respect to prediction while it is vice-versa with respect to correctly fitted models and with respect to correctly shrunk zero coefficients. In the weighted scenarios, WQR-ALASSO and WQR-AE-NET dominate their respective non-adaptive versions as follows; with respect to correctly fitted models, in 62% of the time while with respect to correctly shrunk zero coefficients in 100% of the time in both cases. At the design matrix with both collinearity and high leverage points under the heavy-tailed distributions (t-distributions with d∈(1;6) degrees of freedom) scenarios, the dominance of the adaptive procedures over the non-adaptive ones is again evident. In the unweighted scenarios, the procedures QR-ALASSO and QR-AE-NET outperform their non-adaptive versions as follows; in prediction, in 75% and 62% of the time; with respect to correctly fitted models, they perform better in 100% and 88% of the time, while with respect to correctly shrunk zero coefficients, they outperform their non-adaptive ones 100% of the time in both cases. In the weighted scenarios, WQR-ALASSO and WQR-AE-NET dominate their non-adaptive versions as follows; with respect to prediction, in 100% of the time in both cases; and with respect to both correctly fitted models and correctly shrunk zero coefficients, they both do 88% of the time. Results from applications of the suggested procedures to real life data sets are more or less in line with the simulation studies results.

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“…In order to analyze whether outliers play a dominant role in the model, a combination of leverage and Cook's distance was implemented. The leverage is a distance between an explanatory variable value and the average of the explanatory variable values in the entire dataset (Ranganai, Van Vuuren, & De Wet, 2014). The i th leverage hi is denoted with the following equation:…”

Section: Estimated Time Of Arrivalmentioning

confidence: 99%

Inference of Transit Passenger Counts and Waiting Time Using Wi-Fi Signals

Videa,

Wang

2021

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Passenger data such as real-time origin-destination (OD) flows and waiting times are central to planning public transportation services and improving visitor experience. This project explored the use of Internet of Things (IoT) Technology to infer transit ridership and waiting time at bus stops. Specifically, this study explored the use of Raspberry Pi computers, which are small and inexpensive sets of hardware, to scan the Wi-Fi networks of passengers’ smartphones. The process was used to infer passenger counts and obtain information on passenger trajectories based on Global Positioning System (GPS) data. The research was conducted as a case study of the Streamline Bus System in Bozeman, Montana. To evaluate the reliability of the data collected with the Raspberry Pi computers, the study conducted technology-based estimation of ridership, OD flows, wait time, and travel time for a comparison with ground truth data (passenger surveys, manual data counts, and bus travel times). This study introduced the use of a wireless Wi-Fi scanning device for transit data collection, called a Smart Station. It combines an innovative set of hardware and software to create a non-intrusive and passive data collection mechanism. Through the field testing and comparison evaluation with ground truth data, the Smart Station produced accurate estimates of ridership, origin-destination characteristics, wait times, and travel times. Ridership data has traditionally been collected through a combination of manual surveys and Automatic Passenger Counter (APC) systems, which can be time-consuming and expensive, with limited capabilities to produce real-time data. The Smart Station shows promise as an accurate and cost-effective alternative. The advantages of using Smart Station over traditional data collection methods include the following: (1) Wireless, automated data collection and retrieval, (2) Real-time observation of passenger behavior, (3) Negligible maintenance after programming and installing the hardware, (4) Low costs of hardware, software, and installation, and (5) Simple and short programming and installation time. If further validated through additional research and development, the device could help transit systems facilitate data collection for route optimization, trip planning tools, and traveler information systems.

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Multiple Case High Leverage Diagnosis in Regression Quantiles

Abstract: Regression Quantiles (RQs) (see Koenker and Bassett, 1978)

Cited by 7 publications

References 26 publications

How Do Energy Use and Climate Change Affect Fast-Start Finance? A Cross-Country Empirical Investigation

How Do Energy Use and Climate Change Affect Fast-Start Finance? A Cross-Country Empirical Investigation

Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET

Inference of Transit Passenger Counts and Waiting Time Using Wi-Fi Signals

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